Addition of Vectors: Finding the Angle

[Haftred]

One of my review questions is the following:

"A box is pulled along the floor by a horizontal force of 35 N. Another force acts concurrently on the box with a force of 25 N at an angle of 40 degrees above the horizontal in the same direction as the first force. What is the sum of the two vectors?"

I got the magnitude of the vector to be 56 N by finding the square root of the horizontal and vertical components respectively squared. However, how does one find the angle. I know I need to calculate the inverse tangent of something - but what?

 

[christinono]

Try breaking the vectors down into their x and y components. Then find the sum of the x components, then the sum of the y components. Then, draw a triangle with these vector sums and use trig to find the resultant vector.

 

[Haftred]

thanks...I'll definitely do better on the exam now

 

[christinono]

glad I could help!

 

[Tom McCurdy]

note be sure to add in the extra degres when using a triangle for trig
you can solve for the angle but then you may need to add/subtract 90,180,270,360

 

[Tom McCurdy]

example
--------------=--------------------
--------------=-------------------- ROUGH DRAWING
--------------=--------------------
--------------=-------------------- VECTOR ONE= positive x
--------------=-------------------- VECTOR TWO= negitive y
--------------=--------------------
============AAAAAAAAAAAAAAA
--------------A-A------ If you solve for this angle and you have
--------------A-- A----------counterclockwise movement then you must
--------------A----- A------- subtract 360 to get angle
--------------A-------- A
--------------=-------------------
--------------=-------------------
--------------=-------------------

I hope this makes sense
i know it is very rough sketch